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Coronal heating by low frequency wave-driven quasi-2D MHD turbulence cascade

Coronal heating by low frequency wave-driven quasi-2D MHD turbulence cascade. W. H. Matthaeus. SHINE 2007 – Whistler BC 30 July 2007. Will use four types of models of basic physics of coronal turbulence: “box” models Phenomenological models Full RMHD in expanding geometry

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Coronal heating by low frequency wave-driven quasi-2D MHD turbulence cascade

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  1. Coronal heating by low frequency wave-driven quasi-2D MHD turbulence cascade W. H. Matthaeus SHINE 2007 – Whistler BC 30 July 2007

  2. Will use four types of models of basic physics of coronal turbulence: • “box” models • Phenomenological models • Full RMHD in expanding geometry • Compressible 3D MHD periodic geometry

  3. Parker (1972), Priest et al (1998), Einaudi et al (1996)... Parker (1991), Axford and McKenzie (1995)

  4. [McKenzie et al, 1995; Axford and McKenzie, 1997]

  5. Incoming wave Refracted wave Region of shear B0 K3 u ¢r u K2 Modulated at frequency = (K3-K1)¢ B0 K1 B0 K3 If K2¢B0 = 0 this is  = 0 interaction K2 K1

  6. Model: - Low frequency waves propagate upwards at the coronal base - Inhomogeneity cause REFLECTION - Counterpropagating interact, drive a low frequency “Reduced MHD” cascade - Turbulent dissipation is sustained; Efficiency = Turbulent Dissipation/Flux Supplied Rate of transmission: Alfven Speed / parallel “box” length Rate of Reflection: Rate of turbulent dissipation

  7. Coronal phenomenology • Detail of transverse structure is suppressed -- modeled by turbulence phenomenology • Perpendicular energy containing (correlation) scale controls turbulence • Propagation, reflection and boundary effects are like 1D waves

  8. RMHD (Box): Broadband spectra, random transient reconnection/current sheets T=100 Magnetic field and current density Velocity field and vorticity PDF of Electric current density: Intermittency

  9. Efficiency of 10-50% or moderate to high R, fixed T=1 Dissipation --> 0 if R=0 But Steady dissipation is insensitive to initial seed turbulence level Box model with R and T RMHD simulation Phenomenology

  10. RMHD simulation with coronal profile • Radial expansion • R=Rm=600 • Forcing at bottom • single low frequency 0.1/TA • broadband in Kperp • Waves escape from top and bottom

  11. Comparison of three simulations Comparison of three expansion/RMHD simulations with different density profiles Heating/volume is ~exponentially confined

  12. Conclusions: low frequency wave-driven MHD turbulence as a candidate mechanism for heating the open field line corona • Low frequency waves + reflection = RMHD cascade = sustained turbulent heating • Turbulent heating is insensitive to • initial conditions • many details of the fluctuations • Turbulent heating is sensitive to • reflection • boundary conditions --- “non-propagating “ modes • Heat function • determined by coronal density profiles • approximately exponential with L= Rsun/3 for isothermal gravitationally stratified atmosphere • Efficiencies of 10% - 50 % are easily attainable • Kinetic mechanisms to absorb energy at high kperp are not yet identified

  13. TEST PARTICLE Protons after ~1 nonlinear time Highperpendicular energy B0 B0 TEST PARTICLE Electrons after ~1/10 nonlinear time High parallel energy Out of page B0 B0

  14. Coronal heating by low frequency/quasistatic driven cascade is promising Can we develop a full coronal model that converts low frequency wave energy into a turbulent cascade that produces rapid and sustained heating?Can a model of this type accelerate the wind?Can a model of this type produce the observed kinetic plasma signatures? self consistent models are needed!

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